Techniques are provided for determining an initial attitude quaternion transform, for example based on measurements from a combination of rate sensors, accelerometers, and an inertial reference sensor.
An inertial navigation system (INS) is used to direct a vehicle from one point to another. An INS measures changes in velocity through the use of accelerometers and rate sensors (e.g., gyroscopes). An INS extrapolates a vehicle's position, velocity and attitude by processing changes in the vehicle's motion sensed by inertial instruments. In order to extrapolate position, velocity and attitude correctly, an initial heading of the vehicle relative to an inertial reference frame is needed. If the initial attitude of the vehicle is known precisely, then this can be input to the INS and the extrapolation can proceed. However, if the initial attitude is not known, then an initial inertial reference indication is needed.
Typically, accelerometer readings of the gravity vector and magnetometer readings of magnetic North are used in an Euler angle solution algorithm to provide an initial quaternion for extrapolating position, velocity and attitude. However, the Euler angle solution is complicated and suffers from a singularity when one of the accelerometer axes is aligned with the gravity vector, which is the case for vehicles including, for example, vertical launch vehicles. This singularity prohibits the use of the Euler angle solution.